1

Charmless Three-body Decays of B Mesons

Chun-Khiang ChuaChung Yuan Christian University

HEP2007, 20 July 2007, Manchester

2

Introduction Many three-body B decay modes are observed with rate

s~10-5.

These modes usually have non-negligible (sizable) nonresonant (NR) contributions.

Some modes, KSKSKS, K+K-KS, are useful for the extraction of sin2eff

Most theoretical works are based on flavor symmetry. (Gronau et al, …)

We (Cheng-CKC-Soni) use a factorization approach to study these modes (FA seems to work for DKK decay) A global analysis

SSS

SS

KKKKKKKKB

KKKKKKKB

,,,

,,,0000

3

Different topological decay amplitudes

Treebu

Penguinbs, d

4

Factorized into creation and transition parts

Creation

Transition

Annihilation

Penguinbs, d

Treebu

5

b→s b→u

A brief look at a typical three-body amp.

The creation part <0→K+K-> is related to the kaon’s e.m. form factors, fitted from

data Non-resonant part is constrained by KSKSKS rate and K+K- mass s

pectrum

The transiton part <B0→K-K0> Use HMChPT amplitude with exponential form momentum depen

dence (NR fixed from rate)

0|| jKK

1232 ).( ipppHMChPT eeAA BNR

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B0 to K+K-K0 rate:

Final state Expt (10-6) Theory

K0 2.98±0.45 2.6+0.5-0.4

f0(980)K0 9.57±2.51 5.8+0.1-0.5

X0(1550)K0 0.98±0.44 0.93+0.16-0.15

NR 26.7±4.6 18.1+5.1-3.9

total 23.8±2.6 19.8+0.6-0.6

NR rates: 88% from b→s (via <K+K-|ss|0>)

and 3% from b→u transitions

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b→s

b→u

The b→s transition prefers a small m(K+K-)

Low mKK peak due mainly to KS

The b→u transition prefers a small m(K+K0) and hence large m(K+K-) ⇒ tiny interference between b→s & b→u transitions

b→s

b→u

CP-odd K+K-KS decay spectrum

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low mKK peak: f0(980)KS + NR

peak at mKK 1.5 GeV due to X0(1550)

b→s

b→u

CP-even K+K-KS decay spectrum CP-even+CP-odd

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K+K-KS(L) & KSKSKS(L) rates KS KS KS rate is used as

an input to fix the NR amplitude in 0→KK creation (denoted the parameter)

SD rates agree with data within errors c quark not considere

d yet a small room for LD c

ontribution

1st error: ms, B→K form factors,

2rd error: NR

01.001.001.002.0

theory

01.001.001.002.0

expttheory

03.037.103.019.1

06.014.006.006.0excluded

09.046.010.032.0

11.082.114.049.1

20.028.223.081 .1

expt6

theory6

98.0

07.091.098.0

1463.7

9.02.6input

)14.0( )(

57.1 )(

33.8 )(

2.14.1289.9

)10()10(state Final

L

S

LSS

SSS

K

CPS

CPS

S

KKK

f

KKK

ff

KKK

KKK

CP

KKK

KKK

KKK

BB

S

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B-→K+K-K- decay

The predicted NR rate agrees with Belle The nature of broad X0(1550) (or fX(1500) by Belle) i

s not clear. The large fraction of X0(1550), 121% by BaBar and 63% by Belle, is entirely unexpected, recalling that it is only 4% in K+K-K0

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B→K decays

The predicted NR rate agrees with Belle

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B0→K-+0 decay

1st theory error: NR 2nd theory error: ms, NR, form factors 3rd theory error: Calculations for K-KSKS, KS-0, KS00, KS+- modes

are also available

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B→KK and Sdecays

KK rate agrees with BaBar and Belle rate is sensitive to B → transition (can be used to fix the NR

parameter)

B0→+-0 is predicted to have a rate (Br=26.310-6) larger than +-

- as it receives +, - and 0 resonant contributions

B-→K+K--

B-→+--

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sin2 is naively expected in K+

K-KS due to color-allo

wed tree contribution, tied to NR amplitude

S, ACP are small in

KSKSKS: no b→u tree

diagram

05.000.007.003.0

04.001.005.001.0

40.153.010.154.0excluded

47.152.001.155.0

40.153.010.154.0excluded

008.0000.0019.0000.0

008.0000.0019.0000.0

12.009.0

009.0001.0020.0001.0excluded

008.0007.0019.0004.0

12.009.0

009.0001.0020.0001.0excluded

eff

77.0

1514 69.0

91563.4)(

86.4)(

91563.4)(

Expt.(%)(%)

718.0

20.058.0719.0

13.058.0728.0)(

726.0)(

13.058.0721.0)(

Expt.2sinState Final

LSS

SSS

KL

CPS

KS

f

LSS

SSS

KL

CPS

KS

KKK

KKK

KKK

KKK

KKK

A

KKK

KKK

KKK

KKK

KKK

L

S

L

S

CP asymmetries in K+K-KS, KSKSKS

sin2=0.6780.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

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sin2eff=sin2eff-sin2charmonium

theory expt

sin2(K+K-KS) =0.050+0.028-0.033

-0.098+018-0.16

sin2(KSKSKS) =0.041+0.027-0.032 -0.098±0.20

sin2(KS00) =0.051+0.027-0.032 -1.3980.71

sin2(KS+-) =0.040+0.031-0.032

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Conclusions It is important to understand the NR amplitudes in 3-body de

cays. We have identified two NR sources. We found large NR signal (35%~40%) in K modes, in favor

of Belle measurements Contribution of X0(1550) to K+K+K- should be clarified Intermediate vector & scalar meson contributions to 3-body

decays are identified. The total rates of 3-body B decays are calculated for the first time

Final-state rescattering known to be important for penguin-induced two-body mode

s some FSI effects for 3-body modes are incorporated in the propagator of resonances LD c-penguin, u-penguin

Full Dalitz plot analysis will be very helpful